Name

"Super Wii." Kind of lame but it will be the Wii's SNES. Basically a suped up Wii.

Hardware

CPU: 45nm process, 1 billion transistors, based on POWER7 SCM with 4 active cores, 3GHz Frequency, 256KB L2 cache per core, 2.6MB of FLR-L3 cache per core, 16MB of PSRAM, Enhanced Cache Mode

RAM: 4GB DDRL3 LRDIMM main memory at 800Mhz 

GPU: 28nm process, 825MHz engine frequency, 795MHz memory frequency, 1GB GDDR5 memory

Storage: 250GB 2.5" 7,500RPM disk drive, slot loading optical discs (25GB per layer, up to four layers). External hard drives can be used

Ports: SD memory card slot, 3 USB 3.0 ports (2 in front, 1 at rear), sensor bar power port, HDMI 1.4 out port, ethernet port

Video: 1080i/p, 720p, standard 4:3 and 16:9 anamorphic widescreen, AV Multi-out port supporting composite video

Audio: Supports 48GHz 24-bit audio, 64 bit audio processing, Dolby Digital 5.1 and TrueHD, 22.2 surround sound

All this would cost around $360 so the console could still sell for $349 at launch, with a $50 price cut during holiday 2013 and to $249 by 2015.

Controller

Regular gamepad, comfortable like the GameCube controller but updated. If need a gimmicky controller, a Razer Hydra copy would be okay I guess.  Also work on virtual reality, like the rumored Revolution. See Nintendo On. That's what the main gimmick focus would be on (instead of stupid tablet controllers).

First party games

The main problem with Nintendo first party titles this gen is lack of HD training (according to Miyamoto) and smaller dev teams. I would get them trained on HD and increase teams to make sure games come out on time and hardly any delays. Here is what I would aim for:

Launch titles: Wii Sports, New Super Mario Bros., Pikmin 3, Nintendo Land

2013: Q1-Q2 - Super Mario 64 2 (not 3D World, but a full fledged HD Mario adventure), Zelda Wind Waker HD, Donkey Kong: Tropical Freeze. Q3-Q4 - Retro first person shooter original IP to compete with Halo/Gears/Titanfall/COD, Mario Kart 8, Wii Fit (but make it a killer app like FitBit instead of a throwaway title)

2014: Q1-Q2 - Smash Bros. 4, Star Fox, Fantasy Life (for consoles), Mario Party 10. Q3-Q4 - Zelda with OOT/TP graphics, new Shigeru Miyamoto IP (killer app status hopefully, a swan song), Xenoblade X, Splatoon, Kirby, Yoshi's Wooly World

2015: Q1-Q2 - Animal Crossing, new Nintendo adventure IP, racing simulator (Project Cars buyout?), Level 5 RPG. Q3-Q4 - Metroid, Pokemon MMORPG, Super Mario 3D World, and a 30 year anniversity of Super Mario with 1, 2, 3, World, and 64, Sunshine, Galaxy 1 and 2 getting HD remakes plus Mario Maker, new Wii series game for casuals, Retro Studios FPS sequel

2016-2018: New New Super Mario Bros., new IP, sequels to Splatoon and Kirby, Wario game, Fire Emblem, Earthbound, new IP, another Zelda (probably 2017)

Also try to appeal more to women and older folks with some casual games.

Second/Third Party

Final Fantasy XV and Kingdom Hearts III could have been exclusive to the PS4, but I think both would be impossible so I'd go for Kingdom Hearts timed exclusitivity. Also try and go for Titanfall before EA and Microsoft, Sunset Overdrive maybe. I'd try for Street Fighter V/Mega Man Legends 3 or Rise of the Tomb Raider. Basically, open that huge checkbook Nintendo had in 2010/11.  Hopefully get a couple good third party exclusives.

Also increase support for third party by marketing games for them. That's one reason third parties love Sony/MS, they do a lot of advertising for them. For example, Destiny, Assassin's Creed, and Call of Duty bundles. Do something like that for third parties. Support them so their games are bought on the console.

I'd also increase second party relations and try to broaded the Nintendo demographic. Nintendo is kinda doing that with Bayonetta 2 and Devil's Third now, but I'd also go for western developers like Obsidian. Also would have bought a THQ studio if possible - like Relic or Kaos.

Online

Typical features: username, up to 500 friends, achievements (coins instead. Up to 100 coins for a Power Star), video streaming, ability to group friends in different categories, sort friends by games played, reputation and SmartMatch system similar to Xbox Live, can change username once for free, party chat

Virtual console will be the best. I'd try to get practically every Nintendo game ever published on there if possible and most third party games as well. Thousands of games would be the goal.

Miiverse will be improved, and more social and more conected with Facebook/Twitter/YouTube, Live Gaming Ap (watch others play), video editor then upload, live gaming poll

Multimedia support (Hulu, Netflix, all that jazz), App support in general, backward compatibility with Wii and GameCube games, Easy to Navigate UI, Battery Indicator on Home Screen, Voice command features (like Kinect), ability to stream music/video/pictures from NAS/Shared Folder/DLNA

PS4

Backward compatibility

There would be cooling issues if the Cell processor was included in the system, so if it's possible to do it (the cell processor costs only like $25 now) then the PSU would be external for now until PS3 emulation can be decent enough to be released. If PS3 emulation could be decent before release of the PS4, and could get a decent amount of emulation profiles for it by launch (over 200 top selling games) like the 360's BC then I'd focus on software emulation.

If software emulation and internal BC is not realistic, then here would be an add-on module with an embedded Cell/RSX graphics chip that would connect to the back of the PS4 via an external PCI bus adapter so it can have access to the PS4's I/O and AV-Out subsystems. 

The x86 architecture is fast enough to handle the subsystems necessary to emulate the PS3 properly, due to having 512MB of the memory it needs. This add on would cost about $50 and would attach itself like that ugly Nyko hard drive add on thing (plus smaller and better looking lol) or can be plugged in and hidden, whichever.

All PS4's will be BC with PS1 and PS2 games via emulation.

Hardware

Hardware is fine as is, but maybe soup up the CPU a little bit (2GHz/1GHz like you said), a Sata 6 hard drive, and MAYBE (depending on price) 2-3GB extra RAM for OS support like you said. 8GB GDDR5 though costs a TON of money, so it may not be feasible. Really though the hardware is pretty much perfect, just a little more power in the CPU. It'd be a loss but I'd include the PlayStation camera, mainly for non-gamer type games and voice recognition.

PlayStation Network

PSN is free, but super basic. Basically, you get online multiplayer, albeit not as good connections and tons of ads. Some of them even intrusive (gotta make money somehow). For example, video ads on the dashboard, and ad notifications during gameplay. And there will be limitations: no party chat for free PSN, only up to 100 friends, limiting messaging. 2 accounts per console only. Basically barebones online, but Sony can still make an argument they have free online.

PSN+ will have a ton of features. Instant game collection and discounts of course - and good ones too (way better than now). Exclusive and early released demos. Shareplay/family sharing plan. SmartMatch matchmaking/reputation system/better matchmaking period (better connections), faster downloads, ability to download multiple things at a time, party chat, unlimited friends, can change username for free once, 12 accounts per console, update in the background, no ads, ability to categorize friends, etc. etc.

PlayStation Home will be retooled as a social network for gamers. Kind of like Miiverse. People can comment on your profile/rate you (and you can dispute lol), you can put your favorite stuff on your profile plus a wish list, a list of your trophies, custom background/pictures for profile, basically a far better Miiverse with Twitter/YouTube/Facebook intergration as well.

Controller

Make it super comfortable, put the analog sticks in the right places (like Xbox/GameCube), touchpad will be a touchscreen instead. Better triggers + rumble. Motion controlled I guess.

Project Morpheus would be a priority too. I think VR is gonna be huge so I'd R&D that to heck and hopefully get it out by mid-2015/before the Oculus Rift. And then have some killer apps ready for it.

First/Second party games

Honestly I would have delayed The Last of Us and have it released as a PS4 exclusive. Naughty Dog loves to start each generation with a new IP and The Last of Us would have been a perfect way for them to open up the PS4 generation.

Have Sanzuru or another developer (High Impact?) work on a Jak and Ratchet crossover. Support Insomniac's Sunset Overdrive. GO AFTER TITANFALL! This was a huge mistake on Sony's part. Sony just can't do FPS right. Killzone is a failed series, Resistance also. No matter how much Sony tries, they can't get it. What I would have done is launch the system with Killzone, but also grab Titanfall and have them release it November 2014 with a single player + more game modes. I think Titanfall has (had?) potential to be a new Gears of War/Halo in terms of popularity.

Gran Turismo 6 for PS4 instead. A Level 5 RPG. Try and form a new partnership with a WRPG developer (Obsidian for example), or have Guerilla Games and/or Sony Online create an exclusive WRPG for the PS4 to rival other WRPGs. WRPG is a huge genre now and PS would have a good exclusive.

New Sony Santa Monica IP. A new Syphon Filter.  GET THE LAST GUARDIAN OUT! That'd be a priority! A new IP like Eight Days could be popular.

Third party games

Try to keep Metal Gear Solid V console exclusive, that'd be a priority. I would pay for it and even co-develop it to get it out by 2014. Final Fantasy XV was offered to be a Sony exclusive but Sony probably couldn't afford it, but I would've went for Kingdom Hearts III which may have been a possibility since Kingdom Hearts Remixes were exclusive to the PS3. MAYBE at most make Final Fantasy XV a timed exclusive if affordable.

Street Fighter V of course would be exclusive. Maybe have another third party exclusive deal with Capcom, like for Mega Man Legends 3 or an exclusive Resident Evil game (not necessarily a main series one). Then try to get an exclusive (console) Square Enix RPG - new series or not. Namco is already developing an exclusive Tales Of game. Persona 5 exclusive of course. Maybe work out a huge timed (console) exclusive with a western developer (Mass Effect 4? Star Wars KOTOR? Fallout 4? Something like that). 

So imagine by the end of 2015 the exclusive list will be something like: Killzone: Shadow Fall, Knack, LBP3, Gran Turismo 6, DriveClub, Bloodborne, The Order, The Last of Us, Jak and Ratchet platformer (or just a separate J&D game, and a R&C game), Infamous: Second Son, Titanfall, Kingdom Hearts III, Metal Gear Solid V (console exclusive), a few JRPGs (Tales Of Zestiria, Persona 5, Square Enix RPG, Level 5 RPG like Ni No Kuni), Eight Days, The Last Guardian, Street Fighter V, timed exclusive western game, wow that system would be amazing. PS2 status right there but even better.

Non-Gamers

I'd also try to attract non-gamers. Have social games, tons of indies, and also dance/simulation/fitness games that are popular with the female and older demographic. Research shows that women prefer those type of games. Basically I'd release games to try and appeal to women and try to get some exclusive deals like with Frozen.

And that's not impossible. 33% of Nintendo 3DS owners are women, because it has games that appeal to them like Animal Crossing (56% female userbase), Fantasy Life, Tomadachi Life, Style Savvy, Disney Magical World, Nintendogs + Cats, etc. etc.

As I said, not make it a real focus but try and expand the demographics a little bit. Only around 10% of PS3 gamers were female, the goal would be to try and increase that to around 20-25%.

Other stuff

USB support for headphones
Custom themes
Tons more applications
Upload straight to YouTube
3D Blu-ray support
MP3, MKV, FLAC, CD support
Local media support like DLNA
More seamless PlayStation Store (it's confusing now) and UI

Wii U: Smaller price, Different name, actual advertising, acknowledge third parties,
XB1: Not have the Kinect 2.0 be a thing, 400$ being the launch price, also the horrible reveal